[FOM] Re: Definition of "large cardinal axiom"?

[Dmytro Taranovsky]

An issue in meta-theory of large cardinal axioms is how to deal with
statements like "there is kappa such that the following holds:  kappa is
an inaccessible cardinal and the Continuum Hypothesis is true".  For
statements claiming existence of large cardinals there is a need to
separate the large cardinal axiom component from other components. 
Requiring invariance of the definition under "small" forcing appears to
do this very well, although I do not fully understand why.

Sincerely,
Dmytro Taranovsky